Chap, 90, with a primarily tame pet (4,3)
I believe the answer is:
manx cat
'pet' is the definition.
(cats are often kept as pets)
'chap 90 with a primarily tame' is the wordplay.
'chap' becomes 'man' (chap can mean a man).
'90' becomes 'xc' (Roman numerals).
'with' says to put letters next to each other.
'primarily' suggests taking the first letters.
The initial letter of 'tame' is 't'.
'man'+'xc'+'a'+'t'='MANX CAT'
(Other definitions for manx cat that I've seen before include "Short-tailed feline" , "Tailless pet" , "Tailless animal" , "creature of endless renown" , "Type of feline" .)